sage: fromsage.groups.groupimportGroupsage: G=Group()sage: G.category()Category of groupssage: G=Group(category=Groups())# todo: do the same test with some subcategory of Groups when there will exist onesage: G.category()Category of groupssage: G=Group(category=CommutativeAdditiveGroups())Traceback (most recent call last):...ValueError: (Category of commutative additive groups,) is not a subcategory of Category of groupssage: G._repr_option('element_is_atomic')False

connecting_set – (optional) list of elements to use for
edges, default is the stored generators

OUTPUT:

The Cayley graph as a Sage DiGraph object. To plot the graph
with with different colors

EXAMPLES:

sage: D4=DihedralGroup(4);D4Dihedral group of order 8 as a permutation groupsage: G=D4.cayley_graph()sage: show(G,color_by_label=True,edge_labels=True)sage: A5=AlternatingGroup(5);A5Alternating group of order 5!/2 as a permutation groupsage: G=A5.cayley_graph()sage: G.show3d(color_by_label=True,edge_size=0.01,edge_size2=0.02,vertex_size=0.03)sage: G.show3d(vertex_size=0.03,edge_size=0.01,edge_size2=0.02,vertex_colors={(1,1,1):G.vertices()},bgcolor=(0,0,0),color_by_label=True,xres=700,yres=700,iterations=200)# long time (less than a minute)sage: G.num_edges()120sage: G=A5.cayley_graph(connecting_set=[A5.gens()[0]])sage: G.num_edges()60sage: g=PermutationGroup([(i+1,j+1)foriinrange(5)forjinrange(5)ifj!=i])sage: g.cayley_graph(connecting_set=[(1,2),(2,3)])Digraph on 120 verticessage: s1=SymmetricGroup(1);s=s1.cayley_graph();s.vertices()[()]